Can they carry a day’s worth of food or a week’s worth? Even when spread among several riders, you may have to consider a few pack animals to help carry the load but remember that even then they will not be carrying a month’s supply of provisions or probably a very wide-spread fare.

Three things here: (1) You probably can carry a month’s worth of food if you know exactly what you must carry (and you accept that, indeed, it won’t be a very wide-spread fare,) (2) notice that pack animals are mentioned, but not that they also have to eat (and they eat a lot,) and most importantly, (3) water is not mentioned.

It’s easy to forget, thanks to modern amenities, but water is even more important and a worse logistical nightmare than food is. Some well-disciplined pre-modern armies like the Romans carried their own food (mostly grain,) but rarely hauled water. It would simply be unsustainable.

I’m aware that essentially no fiction story, whether it’s fantasy, science fiction, or even historical, bothers with these things. It’s pretty much the standard of fiction to ignore these issues, and even if you happen to come across someone who cares about these necessities, it will usually be one of the three elements required —food, water, and fuel (wood)— but not the three at the same time. So I’m not writing this as a way to lash out against books that fail to keep in mind these things because then I’d have to dismiss pretty much 99% of everything that has ever been written.

To follow up on the three points above…

(1) I wouldn’t recomment it, but you probably could carry a month’s worth of food (notice I didn’t say supplies.) However, you’ll have to settle for bread. A lot of bread. In fact, not even bread but grain, because you’ll have to mill and bake it yourself. So the worse problem may be having to carry a small grain mill, not the grain itself (but that’s where the donkey/horse comes for,) and all the time you’ll have to invest in preparing your food. That’s what the Roman legionaries did, by the way. Each unit of eight soldiers had their own mill, mule, and tent, and it seems that they prepared their own food.

To feed someone (let’s assume, a man) who is strong and very active, like in the military (which is a good analogy for an adventurer in a fantasy setting) you’ll need (and this is the low end) something like 3,000-3,500 kcal per day—more for more active days. On average, you could probably accomplish that with 3 pounds of foodstuff, 80% of it being grain-based. Simplifying, if you can carry 1kg of grain per day, so 30kg for a month, you can carry the bulk of your monthly food needs (and, remember, modern soldiers carry more than that in weight.) Not the best fare, but you won’t starve.

It’s not a pleasant scenario and I wouldn’t recommend going around with an entire month’s supply of anything, but it can happen. And if you don’t like carrying so much wheat or flour around, you can always hoard hardtacks. Going back to the Roman soldiers, their diet was probably 80% or so grain (bread,) the rest being meat, beans, vinegar, oil, salt, and other extra things and whatever the local area produced. But the fuel of any pre-modern army was bread (or rice for other cultures, I guess.) You’ll just need a good backpack and excellent weight distribution to carry it. An in any event, maybe not a month’s supply, but you could certainly carry a week’s supply in hardtacks. I hope you like them.

(2) If you want to travel a bit more confortably, you’ll need a pack animal. Unfortunately, and as writers easily forget, these animals are not cars. They also need to eat and drink. Remember, a horse may need from 25-40 liters of water per day. And as for food:

According to the Ontario Ministry of Agriculture, a full-grown horse should eat about 15 to 20 pounds (6.8 kg to 9.1 kg) of hay a day. That is 1.5 percent to 3 percent of its body weight if it weighs about 1,000 pounds (450 kg). This is a very rough average and horses will require more or less depending on their metabolism, workload, the time of year, and what else they may be eating.

Source

You obviously are not going to carry the horse’s food on your back, although the animal could carry part of its own food (but I’d recommend a wagon for that.) You can let it graze, of course, but you can’t graze in all seasons and, besides, their entire diet shouldn’t be random grasses.

Donkeys and mules are less demanding, so they make better pack animals than horses.

(3) But the worst problem is still the same whether we are talking about humans or animals: water.

People can survive without food for a long time, but not without water. A modern person is said to require 2 liters of water per day, but that’s because we are sedentary couch potatoes. Anybody who has an active life or work (like adventuring) is going to need way more than that, from 3 L to 5 L or more. In weight, that’s a lot more than your daily food requirements.

On top of that, add the water you’ll need for cooking because you’ll need some too for whatever grains you have available, and you’ll want to cook them in one of the two basic ways: (a) as a porridge or (b) as bread. If then you add the ridiculous amounts of water a horse needs, you realize that what will limit your character’s movements and logistics is not so much food as water (and if the setting is cold, a lot of wood for fuel.)

If you have ever wondered why so many battles in history happened along rivers, now you know. Armies pretty much followed rivers and lakes, or the sea if they had a fleet of supply ships tagging along the coast (and these can carry water for the soldiers.) And armies are not just people but animals too (and lots of them.) For a roman army, expect one mule for every 4-5 soldiers, which means that an army of 10,000 soldiers would have 2,000-2,500 mules with it, plus oxen and horses. That’s, assuming 3 liters per person/day and, to simplify, 20 liters for each mule, 70,000-80,000 liters of water per day. That’s just the bare necessities. So without an entire fleet of tanker trucks, you’ll need to follow natural sources of water.

All of this has some implications for the writer who cares about such things. Some of these may be:

-Almost nobody, at least large groups of people, will willingly wander more than 2 miles away from any known source of water. What that means is that, yes, the world may be big, but in practical terms, it’s actually quite small and you can guess where someone will go if you know the territory and that they need to eat/drink.

-Cut off anybody from said source of water (or poison or destroy it,) and they are doomed.

-If the story is set in some place where water is not readily available for whatever reason, people will not willingly go there unless they can prepare an entire expedition, which means not just pack animals but draft animals too. So, in real life, to “go to buy some provisions” for an adventure doesn’t mean “some iron rations” but a large cart holding 500 L of beer water

-Just carrying a canteen or a water bottle for your character to take occasional sips is going to hold off dehydration for… a day perhaps?

-Monsters and other creatures probably need to drink too, and worse, they know you do.

-Worse yet: they may not need food or water (being magical or undead or whatever) but they know you do. Unfortunately, I don’t remember any story where this angle was developed.

-Before modern sanitation, many sources of water weren’t clean, so many people just drank small beer or watered wine all the time. I guess alcoholism rates were quite high back then.

-What do monsters eat? What can feed an entire army of ravenous orcs? The answer is: lots of humans. This is an obvious fact that I have never seen in modern fantasy although it’s pretty common in ancient mythology. If malevolent creatures of that type exist, and you want to have thousands of them, and since they clearly are not farming the land (and they may be carnivorous anyway)… what do they eat? Well, they eat you. That’s probably why they are called monsters.